Various data transfer systems have been developed including storage systems, cellular telephone systems, and radio transmission systems. In each of the systems data is transferred from a sender to a receiver via some medium. For example, in a storage system, data is sent from a sender (i.e., a write function) to a receiver (i.e., a read function) via a storage medium. Encoding may involve vector multiplication by a quasi-cyclic matrices. Such vector multiplication is complex both in terms of circuit design and the area required to implement the circuits. Such significant area requirements increase the costs of encoding devices.
Hence, for at least the aforementioned reasons, there exists a need in the art for advanced systems and methods for data processing.